biocinematics
commented
2 years ago Hi Mihai,
I'm Stuart, I create 3D animations to communicate science, particularly molecular biology and synthetic chemistry. This project sounds very interesting, as molecular biology and in particular molecular motion is all about Brownian motion. I don't have a deep background in mathematics (just a few undergraduate courses and many numberphile/3blue1brown videos), but I pick things up quickly.
You can check out my work here: https://www.youtube.com/biocinematics And this video in particular may be of interest: https://www.youtube.com/watch?v=JnIkGtkO-Js
I work with Houdini, which is a very powerful animation program that is well suited for science visualization and procedural generation (vs. drawing and building by hand). I currently have many projects on the go, so I hesitate to make any commitments, but I care a lot about mathematics and science communication, so I'd hate to pass up the opportunity to work with a content expert on a very cool video.
I'm happy to chat via email if you'd like to discuss further. I read Grant's tweet just a few minutes ago and kind of immediately jumped in here, so I don't know what the proper procedures are.
Contact details stuart [at] biocinematics [dot] com
PS I attended UofT for a Master's degree a number of years ago.
Edit: Oh, I should also mention that my small claim to fame is a minor contribution to one of Grant's most popular videos. I made the single continuous line image of Fourier himself for the Fourier transform video.
I want to make a math explainer that helps explain why it so mesmerizing to zoom in on a Brownian motion as in this video https://www.youtube.com/watch?v=UT7AG2OoYZo . What is the math behind this?
About the author
I'm currently a professor at a university in Canada in the area of probability and machine learning. Last year I was a runner up in SoME1 for my video on the Buffon Noodle problem https://youtu.be/e-RUyCs9B08 . My websites where you can learn more about me: https://nicam.uoguelph.ca/ http://www.math.toronto.edu/mnica/
Quick Summary
Target audience: High school/early university students who have seen some tame functions but haven't had much experience with wild functions like Brownian motion paths. The fact that these types of function can exist is very exciting (and has the potential for some amazing visuals)!
Video idea: Show the video of Brownian motion zooming to bring up the question of what it is we are looking at and why does it look so mesmerizing (compared to say zooming in on an "ordinary" function?) Bring up the question of why can you zoom in forever and why is it such a "rough" path? Then answer these questions with some math explanations!
Target medium
Video! Being able to make nice animations of the functions (in manim or something else) is a key skill that I am not so good at (I have some very basic manim skills)
More details
The three sections I have in mind: 1. What is Brownian motion? Show the construction of Brownian motion as the limit of piecewise linear functions (Levy's construction). I think this would make a cool visual as you make finer and finer pieces that start to look more and more rough. (see page 10 of this classic book for 3 frames of this https://people.bath.ac.uk/maspm/book.pdf )
2. Why is it a random fractal? Explain why Brownian motion has the scaling property $B_{a^2t} = a B_t$ in distribution, which is why it is a random fractal. (Fractals are self similar when you zoom in: Brownian motion has the same distribution when you Zoom in). This essential comes from the fact about variance that $Var(X+Y)=Var(X)+Var(Y)$ and $Var(aX)=a^2 Var(X)$
3. Why is it continuous but nowhere differentiable? Continuity follows by the construction since it will be uniform limit of continuous functions. To see that its nowhere differentiable we use the self-similarity from point 2 to find a sequence where the slopes get larger and larger. This can also be visualized quite nicely!
Reference book: https://people.bath.ac.uk/maspm/book.pdf
Contact details
Email: mcnica89@gmail.com
Additional context